Is there a way to bake an array animation?
If the software you want to export it to supports alembic (i know for example that fusion does), you can use this fileformat. It was just added to Blender so it only works in the newest Versions. Exporting it in Blender and importing it again works fine and it bakes the animation to mesh cache (In Blender it then uses the mesh cache modifier). This is also how you can export fluid simulations for example.

Just choose File - Export: alembic (.abc) and configure the options (especially the end frame)